Mathematical model for thickness of off-center spin-coated polymer films

Off-center spin coating is a method to fabricate thin film on a substrate where the substrate is located at an off-center distance away from the rotating center of the spin coater. Here, a mathematical model to calculate the thickness of a film fabricated by an off-center spin-coating technique was developed and proposed. The model showed that the off-center film thickness was calculable by using four factors—the on-center film thickness, mass fraction of solid in the wet film, length of the substrate in the radial direction, and off-center distance. Simply, the off-center film thickness was inversely proportional to the off-center distance to the exponent of one-third, that is, the further the off-center distance, the thinner the film. The model was verified where the thicknesses of the films calculated by using the model were compared with the experimental values obtained from the off-center spin-coated films of poly(vinylidene fluoride) at various off-center distances. Both the modeled and the experimental data were of the same trend and in a good agreement with each other, indicating the validity of the model. The limitations of the model were also discussed. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48356.